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Journal Article

Mathematical Analysis of Random Noise-Conclusion

01 Jan 1945-Bell System Technical Journal-Vol. 24, pp 46-156
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
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Journal ArticleDOI
TL;DR: This paper deals with the modeling and analysis of narrowband mobile-to-mobile (M2M) fading channels for amplify-and-forward relay links under line-of-sight (LOS) conditions and the proposed channel model is referred to as the multiple-LOS second-order scattering (MLSS) channel model.
Abstract: This paper deals with the modeling and analysis of narrowband mobile-to-mobile (M2M) fading channels for amplify-and-forward relay links under line-of-sight (LOS) conditions. It is assumed that a LOS component exists in the direct link between the source mobile station (SMS) and the destination mobile station (DMS), as well as in the links via the mobile relay (MR). The proposed channel model is referred to as the multiple-LOS second-order scattering (MLSS) channel model. The MLSS channel model is derived from a second-order scattering process, where the received signal is modeled in the complex baseband as the sum of a single and a double scattered component. Analytical expressions are derived for the mean value, variance, probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the received envelope of MLSS channels. The PDF of the channel phase is also investigated. It is observed that the LOS components and the relay gain have a significant influence on the statistics of MLSS channels. It is also shown that MLSS channels include various other channel models as special cases, e.g., double Rayleigh channels, double Rice channels, single-LOS double-scattering (SLDS) channels, non-line-of-sight (NLOS) second-order scattering (NLSS) channels, and single-LOS second-order scattering (SLSS) channels. The correctness of all analytical results is confirmed by simulations using a high performance channel simulator. Our novel MLSS channel model is of significant importance for the system level performance evaluation of M2M communication systems in different M2M propagation scenarios. Furthermore, our studies pertaining to the fading behavior of MLSS channels are useful for the design and development of relay-based cooperative wireless networks.

5 citations

Journal ArticleDOI
TL;DR: In this article, the applicability of the scintillation index meanings are substantially limited for the assessment of the performance quality of the optical data transmitting channels and the peculiarities of the localized intensity distributions and those of the SCI are revealed on the basis of the experimental data got under different propagation conditions.
Abstract: Theoretical and experimental studies of the local statistical characteristics of Gaussian beams propagated through the paths with strong turbulence were carried out and their results are presented. It is ascertained that the applicability of the scintillation index meanings are substantially limited for the assessment of the performance quality of the optical data transmitting channels. On the basis of the experimental data got under different propagation conditions the peculiarities of the localized intensity distributions and those of the scintillation index are revealed.

5 citations

Journal ArticleDOI
TL;DR: Here, the full space of dimensionless parameters is explored and an "asymptotic phase diagram" is presented which delineates the limiting regimes.
Abstract: We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviors, depending upon the limiting cases which are considered, some of which have been discussed in earlier work. Here, we explore the full space of dimensionless parameters and present an "asymptotic phase diagram" which delineates the limiting regimes.

5 citations

Journal ArticleDOI
TL;DR: In this paper, the authors derived joint probability distributions for the intensity in the output pulse to have values I1 and I2 at times t 1 and t 2 at frequencies ω 1 and ω 2.
Abstract: In the linear regime before saturation, we describe the statistical correlations in the narrow band chaotic output of the self-amplified spontaneous emission free-electron laser. At a fixed position along the undulator axis, we derive joint probability distributions for the intensity in the output pulse to have values I1 and I2 at times t1 and t2, and for the spectral intensity to have values I 1 and I 2 at frequencies ω1 and ω2. Probability distributions for the peak values of intensity in the time and frequency domains are also determined.

5 citations

Journal ArticleDOI
01 Mar 2015-Extremes
TL;DR: In this article, the mean number of continuous and discontinuous crossings through a fixed level on a compact time interval is derived for a process which is the sum of two independent processes: a smooth process and a pure jump process with finitely many jumps.
Abstract: We extend Rice Formula to a process which is the sum of two independent processes: a smooth process and a pure jump process with finitely many jumps. Formulas for the mean number of both continuous and discontinuous crossings through a fixed level on a compact time interval are obtained. We present examples in which we compute explicitly the mean number of crossings and compare which kind of crossings dominates for high levels. In one of the examples the leading term of the tail of the distribution function of the maximum of the process over a compact time interval as the level goes to infinity is obtained. We end giving a generalization, to the non-stationary case, of Borovkov-Last’s Rice Formula for Piecewise Deterministic Markov Processes.

5 citations